De Thou on François Viète

Jacques-Auguste De Thou (1553-1617) was a French historian famed for his work Historia sui temporis written in Latin. In 1604 the first 18 books covering the period up to 1560 appeared. Four further parts appeared so that by 1620 there was a complete edition of history up to 1607. A French translation entitled L'Histoire universelle de Jacques-Auguste de Thou, depuis 1543 jusqu'en 1607, was published in 1634. De Thou was a friend of Viète, so the biographical details he presents in his L'Histoire concerning his friend provide a fascinating insight.

François Viète, born at Fontenay in Poitou, was a profound and original thinker who understood the most secret mysteries of the most abstruse sciences and easily succeeded in all the projects that an intelligent man could conceive and carry out. But among his various occupations, and the wealth of affairs with which his vast and tireless spirit was always aoocpied, he more particularly turned his attention to mathematics, and his excellence was such that all the results obtained by the Ancients, of which time has deprived us by destroying their writings, all these he rediscovered for himself and recalled them to men's minds, sometimes even adding further results of his own.

His powers of concentration were such that he often remained three days together in his study without eating and even without sleeping, except by occasionally resting his head on his hand to refresh himself with a few moments of slumber.

He wrote several books but copies of them are exceedingly rare because since they were printed at his own expense he received all the copies and, being very generous, he gave copies to all who were interested. Apart from his original works, he left many others which shed light on the arts and served to revive the memory of Ancient authors and since Pierre Alleaume of Orleans [a friend of Viète who was left many of his papers - in fact de Thou confuses Pierre Alleaume and his son Jacques Alleaume who was a pupil of Viète] had helped him in his work, Viète's heirs gave him the manuscripts. It is from this rich collection that Alleaume, the Scot Alexander Anderson [a pupil of Viète born in 1582 and died after 1621] and several others have taken the material for many treatises that they have published (to the great admiration of all lovers of mathematics). These works are a living memory to the glory of this great man.

Adrian Romanus proposed a problem to all the mathematicians of Europe and Viète, who was the first to solve it, sent his solution to Romanus with corrections and a proof, together with Apollonius Gallus. Romanus was so impressed by Viète's knowledge that he set out from Würtzburg in Franconia, where he had been living since he had left Louvain, and travelled to France to make Viète's acquaintance. When he arrived in Paris he found that Viète had gone to Poitou for the sake of his health. Roman followed him there, although it meant a journey of about a hundred leagues, and when he finally had the pleasure of meeting Viète he consulted him at length about all the difficulties he had encountered. Such was his admiration for this extraordinary man that he admitted that what he had found exceeded even what he had imagined. Romanus stayed with Viète for a month and left him only with great regret. Viète, wishing to recognise the honour Romanus had done him in undertaking so long a journey to visit him, arranged to pay for his guest's return journey through France.

Moreover, Viète's essay on Apollonius was held in such high esteem that it inspired Marino Getaldi of Ragusa, a very excellent mathematician, to write a book called Apollonius Redivivus. This was published seven years later, with the Apollonius Gallus included as an appendix.

It displeases me much that Scaliger [Joseph Scaliger (1540-1609) was a friend of de Thou] attacked Viète with so much bitterness on the subject of Cyclometrics. But at this time this generous man did not recognise the full merit of his adversary, and thus could not forebear to show resentment when he was corrected by him although he had not in fact fully examined the logic of his own argument. Later he corrected his mistake and with a praiseworthy frankness withdrew his attack. From then on he always had a secret admiration for Viète.

A little before his death Viète, realising that the Lilian calendar [another name for the Gregorian calendar - Lilius was a Veronese doctor working on the reform of the Julian calendar at the time of his death in 1576] had several deficiencies which had already been pointed out by other people, succeeded in designing a reformed version which was suitable for use by the Catholic Church and adapted to its festivals and rituals. This was printed in 1600, and he gave it to Cardinal Aldobrandini at Lyon when he arrived there as the Papal envoy sent to settle the dispute between the King and the Duke of Savoy. But Viète's enterprise met with ill success, as I had warned him it would when he told me about it before he set out. Many people had striven to introduce a reformed calendar in the various states of Christian princes, where such a reform was, finally, accepted after a great deal of effort, but such people make it a rule of statecraft not to admit to having made errors, or even to admit it possible that they should ever have been in error, and they were therefore not willing to accept a change which would make it clear that they had in fact made mistakes in the past.

When peace had been made, Cardinal Aldobrandini returned to Rome, and Christopher Clavius, who had already been occupied with the work of Lilius, rejected the correction Viète had proposed to the Cardinal. Viète then wrote to this famous mathematician, complaining bitterly at his behaviour, and it seems that if he had not died soon afterwards the dispute would not have ended where it did; for those who were not afraid of so redoubtable an opponent after his death would not have attacked him with impunity during his lifetime.

Before this dispute stirred up bitterness between them, Viète had made it clear that he considered Clavius an excellent writer on the elements of mathematics and one who gave lucid and convincing explanations of many obscure passages in original works, although he tended to write as if he had only just become acquainted with the subject matter and made no original contributions to it. He merely copied from the works of others, without acknowledging his debt to the original authors, despite the fact that his own contribution had merely been to collect, arrange and explain what he had found scattered in various places in the books he used, which were, indeed, not always models of order and clarity.

What I am about to add is not important according to Viète's own view, though anybody else would consider it so. The State of Spain consists of several geographically separate parts, and the various communications that have to pass between them, are, for the sake of secrecy, written in various ciphers. When the Spaniards want to change these ciphers they can do so only after considerable time after taking the original decision, because they have to give advance warning of the change to the Viceroys of the Indies.

At the time of the disturbances of the Sainte-Ligue [the Holy League was an association of Roman Catholics, actively supported by the Spanish, opposed to the accession of the Protestant Henry IV] the cipher the Spaniards used consisted of more than 500 different characters and although many exceedingly long letters containing explanations of Spanish plans had been intercepted, all attempts to decipher them had failed, because so many signs were involved. The King [Henry III] had these letters sent to Viète, who had no difficulty in understanding them, nor in understanding all the later ones. This so amazed the Spaniards, and so upset their plans for two whole years, that they proclaimed in Rome, and everywhere else, that the King must have used magic to learn their cipher.

JOC/EFR August 2007

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